MATHEMATICS STDIX TOPIC VOLUME PDF CHAPTER LINK 1

MATHEMATICS STD-IX TOPIC: VOLUME

PDF CHAPTER LINK 1. NCERT TEXT BOOK (CHAPTER- VOLUME)

Learning Objectives Students will be able to 1. understand the importance of volume in our daily life. 2. find volume of solid objects (cuboid, cube, cylinder, cone, sphere and hemisphere)by using formula. 3. solve problem related to volume of solid objects. 4. apply the concept of volume of solid objects in day to day life.

Why will you study volume? �To find capacity of aquarium. �To find how much water does the cylindrical container hold? �To know how much coca cola the cylindrical container hold?

Cont … �To find quantity of ice cream inside the cone. �To know amount of air football holds. �To know capacity of a hemi spherical bowl.

Introduction �If an object is solid, then the space occupied by such an object is measured, and is termed the Volume of the object. �On the other hand, if the object is hollow, then interior is empty, and can be filled with air, or some liquid that will take the shape of its container. In this case, the volume of the substance that can fill the interior is called the capacity of the container.

Definition of Volume �The space occupied by an object is called Volume of the object. � The capacity of an object is the volume of substance its interior can accommodate. �The unit of measurement of either volume/capacity is cubic unit.

Volume of a Cuboid

Cont. . � Cuboid

Volume of a cube �

Example 1 Question : A wall of length 10 m was to be built across an open ground. The height of the wall is 4 m and thickness of the wall is 24 cm. If this wall is to be built up with bricks whose dimensions are 24 cm × 12 cm × 8 cm, how many bricks would be required? (3 Marks)

Solution: �

Example 2 �

� Example 3

Volume of a right circular Cylinder �

Example 4 Question : At a Ramzan Mela, a stall keeper in one of the food stalls has a large cylindrical vessel of base radius 15 cm filled up to a height of 32 cm with orange juice. The juice is filled in small cylindrical glasses (see Figure ) of radius 3 cm up to a height of 8 cm, and sold for Rs 15 each. How much money does the stall keeper receive by selling the juice completely? (4 Marks)

Solution: �

Cont… �

Activity 1: Volume of a Right Circular Cone Objective : To find the volume of a right circular cone Materials required : Chart paper , sand , scissor etc. Procedure: 1. Try to make a hollow cylinder and a hollow cone like this with the same base radius and the same height. 2. Fill the cone up to the brim with sand once, and empty it into the cylinder. We find that it fills up only a part of the cylinder [see Fig. (a)]. 3. When we fill up the cone again to the brim, and empty it into the cylinder, we see that the cylinder is still not full [see Fig. (b)].

Activity 1 cont… 3. When the cone is filled up for the third time, and emptied into the cylinder, it can be seen that the cylinder is also full to the brim [see Fig. (c)]. Observation: We observed that when cone is filling three times the cylinder , the cylinder is completely filled. Conclusion: So we conclude that volume of cone is one third of volume of the cylinder.

Cont. . �

Example 5 �

Example 6 �

Cont. . �

Volume of a Sphere �

Example 7 �

Example 8 �

Example 9 �

Cont… �

Summary �

Mind Map

Learning Outcomes �

Cont… 5. The students arrive at the formula for the volume of a cone through a simple activity, which relates it to the volume of a cylinder. 6. Students learn that the volume of a sphere & hemisphere. 7. Students learn that how to use the volume of these solid objects in daily life situations.